Quantum error correction of continuous-variable states with realistic resources

Abstract

Gaussian noise induced by loss on Gaussian states may be corrected by distributing Einstein-Podolsky-Rosen entanglement through the loss channel, purifying the entanglement using a noiseless linear amplifier (NLA), and then using it for continuous-variable teleportation of the input state. Linear optical implementations of the NLA unavoidably introduce small amounts of excess noise and detection, and source efficiency will be limited in current implementations. In this paper, we analyze the error-correction protocol with nonunit efficiency sources and detectors and show the excess noise may be partially compensated by adjusting the classical gain of the teleportation protocol. We present a strong case for the potential of demonstrable error-correction with current technology.

Continuous-variable entanglement distillation over a pure loss channel with multiple quantum scissors

“…The calculation also applies to the teleportation-based CV error correction scheme with approximate NLA [34], and is computationally efficient. This is in contrast to the Fock basis calculations presented in [32,33], which do not scale well with increasing number of quantum scissors. Our choice of the RCI as the figure of merit is operationally more relevant than those considered before, such as the logarithmic negativity [47,48] and the entanglement of formation (EOF) [49].…”

“…9 (a), the quantity q 1 is plotted, where it has been optimized over a classical gain tuning parameter that scales the dual homodyne outcome prior to the displacement correction operation. We find that our curve for the N = 1−NLA is qualitatively similar, but below what was reported in [33] for the same. This is as expected, since we have consid- Figure 10.…”

“…In addition to the analyses based on the RCI, we also evaluate a Gaussian lower bound on the EOF of the state heralded by a single quantum scissors. We qualitatively validate the findings presented in [33] and extend the analysis to two quantum scissors.…”

“…1 (b) quickly becomes cumbersome with increasing (but finite) N (c.f. [32,33]). In order to make the calculation more tractable, we emulate the quantum scissors by replacing the photon number detectors with ON-OFF photodetection {|0 0| , I − |0 0|}, and the single photon by one mode of a weak TMSV state (of mean photon number µ aux ).…”

“…In the limit of a large number of scissors, NLA can probabilistically distill highly entangled and highly pure Gaussian states from weakly entangled, mixed Gaussian states [30]. Approximate NLA based on a single quantum scissors was further investigated in [32,33] for quantum error correction [34] of CV entangled states, towards designing quantum repeaters [35][36][37]. CV entanglement distillation with a single quantum scissors was experimentally demonstrated in [38].…”